Section 19. How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it
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When I watched my poor Brother be led away to imprisonment, I attempted to leap down into the Council Chamber, either to rescue him, or at least to say goodbye. But like before, I couldn’t move. Somehow my Teacher was holding me in place.
He said to me, sadly, “Don’t worry about your brother. If you’re lucky, you’ll soon have all the time in the world to speak with him. Follow me.”
Once more we lifted up into space. “So far,” said the Sphere, “I’ve only shown you Plane, or Flat Figures and their insides. Now I have to teach you about Solids, or Three Dimensional shapes, and explain to you how we are constructed.
“Here I have a deck of square cards. Watch – I put one on another, and not Northward like you assumed, but On Top Of It. Now I do the same with a second, and a third card. You see? I am building up a Solid by placing multiple Squares parallel to each other. This is the last card, so now this Solid is complete, and it is as high as it is long and wide, so we call it a Cube.”
“Pardon me, my Lord,” I replied, “But to me, it just looks like an Irregular Figure whose inside faces me. I mean, I don’t think I’m seeing a Solid, but a Flat shape, like we imagine in Flatland, but so Irregular that it makes me think it’s some monstrous criminal, to the point that I’m afraid just to look at it.”
The Sphere said, “It appears to you as a Plane Figure, because you’re not used to light, shade, and perspective yet, the same way that in Flatland, someone who does not know the Art of Sight Recognition would see only a Straight Line when they look at a Hexagon. But it is a Solid, as you’ll see through the sense of Feeling.”
[ID: A greyscale diagram showing two cubes. The first has horizontal lines drawn on each face, and dotted lines on the inside to show the perspective, and has a label explaining, “A Spacelander can recognize shading and perspective to understand that a 3D shape is made of multiple surfaces.”. The second cube has the whole inside scribbled in, making it appear more like a slightly stretched out hexagon than a cube, and is labeled, “A Flatlander who does not understand the meaning of perspective or shading will see the 3D object as only a single flat surface.”. Image description end.]
Then he had me Feel the Cube, and I found that he was telling the truth – this amazing creation wasn’t a Plane at all, but a Solid, and it was blessed with six Plane sides, and Eight Terminal Points, called “Solid angles”.
And I remembered what the Sphere had told me, that this shape was created by moving a Square parallel to itself through space, and I felt joy at the thought that a Creature as insignificant as I could, in some way, be called the ancestor of such a remarkable descendant.
But I still couldn’t fully understand what my Teacher meant about “light” and “shade” and “perspective”, so I didn’t hesitate before asking for more information.
I won’t bore you with the details, because I know you Spacelanders are all already experts in it, but the summary is that, through very simple, logical statements, and changing the positions of different objects and lights, and letting me feel these objects, and even his own sacred body, the Sphere succeeded in teaching me the Art of Perspective, so that I could now easily tell the difference between a Circle and a Sphere, and a Plane Figure and a Solid.
((A note from the second editor. I would like to apologize to the author despite the fact that he is long-since dead, because I will have to also edit the following sections for my readers to more easily understand him, so his original wording will not remain intact. To see the author’s original phrasings, please see Flatland: A Romance of Many Dimensions, 1884.))
This was the Climax, the Paradise, the Peak of my strange and eventful life. From now on, I will have to tell you the story of my miserable Fall. Miserable, but undeserved! Because why should those seeking knowledge be teased, only to be disappointed and punished?
My mind shrinks from the painful task of telling you how I was humiliated, but, like a second Prometheus, I will endure this, and worse, if it has a chance of lighting a spark of rebellion in the hearts of Plane and Solid Humanity, against the idea that we should limit our understanding of the Dimensions as only being Two, or Three or anything less than Infinity itself!
I will throw away all my personal feelings! Let me continue my story to the end without any further distractions, or pauses, and just tell you the plain facts of History. The exact facts, the exact words, they are burnt into my brain, and I will set them down without a single change to them, and let my Readers be the judge of me and my Destiny.
The Sphere would have been happy to continue his lessons by teaching me about the conformation, or structure, of all common Solids – Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres, but I decided to interrupt him.
Not because I was bored with his teachings – on the contrary, I wanted even more than he was offering me.
“Pardon me,” I said formally, “O You Whom I must no longer call the Perfection of all Beauty; please, I beg you, let your humble servant have the blessing of the sight of your insides.”
The Sphere: My what?
Me: Your insides, your stomach, intestines.
The Sphere: Where did this suddenly come from? And what do you mean I’m no longer the Perfection of all Beauty?
Me: My Lord, your own wisdom has taught me to look forward to a Teacher even more great, even more beautiful and more close to Perfection than yourself.
Me: As you are superior to all Flatland forms, combining many Circles into One, I have no doubt that there is Another above you who combines many Sphere into One Supreme Existence, going above and beyond even the Solids of Spaceland.
Me: And just as we are in Space looking down on Flatland and can see the insides of all things, I am certain that above us there is an even higher, purer region, where you intend to lead me next, O You Whom I will always call, everywhere and in any Dimensions, my Priest, Philosopher, and Friend/
Me: You plan to bring me to some more spacious Space, some more dimensionable Dimensionality, where we will look down together on the revealed insides of Solid things, and where your own intestines, and those of other Spheres, will lie as exposed to the view of this poor wandering exile from Flatland, who has already been blessed to learn so much.
The Sphere: Pooh! Ridiculous! Enough of this nonsense! We are running out of time, and there’s still a lot you have to learn before you’re ready to teach the Truth of the Three Dimensions to your ignorant countrymen in Flatland.
Me: No, Teacher, please don’t say no to what I know is in your power to give me. Let me have just one glimpse of your insides, and I will never ask for anything else – I will be your perfect and silent student, your forever slave, ready to learn everything you have to teach me without interruption.
The Sphere: Well then, to get you to be quiet, I’ll say once and for all that if I could show you, I would, but I can’t. You can’t really expect me to turn my stomach inside out for you, can you?
Me: But my Lord has shown me the intestines of all my countrymen in the Land of Two Dimensions by bringing me into the Land of Three.
Me: How can it be any more difficult to bring me to the region of the Fourth Dimension, where I’ll be able to look down and see inside of every Three-Dimensional house, the very mines inside the Solid Earth, and the intestines of every living Solid creature, including the noble and blessed Spheres?
The Sphere: But where is this land of Four Dimensions?
Me: I don’t know, but I’m sure you do.
The Sphere: I don’t, there is no such place. The very idea of it is completely ridiculous, it’s inconceivable.
Me: Not inconceivable, my Lord, to me, so surely you must understand it as my Teacher. No, I’m sure you know, I know my Lord will be able to use his arts to explain the Fourth Dimension to me, just like how you explained the existence of the invisible Third Dimension to me while I was in Flatland, even though I couldn’t see it yet.
Me: Let me go back to what you said before. Didn’t you teach me that when I saw a Line and inferred a Plane, I was really seeing a Third Dimension, separate from brightness, called “height” without realizing it?
Me: Doesn’t logic then state that, in this region, when I see a Plane and infer a Solid, I’m also seeing a Fourth Dimension I cannot recognize, which is separate from color, but still exists, though in a way we cannot think to measure?
Me: And let’s not forget we have the proof of the Analogy of Figures, too!
The Sphere: Analogy? Nonsense! What analogy?
Me: Your Lordship is testing to see whether I have been paying attention! But please don’t waste time like this, my Lord, I want – I need more knowledge! Most likely we cannot see that higher Spaceland right now, because we have no eye in our stomachs.
Me: But the Land of Three Dimensions still existed even in Lineland, though that poor Monarch couldn’t turn either way to see it, and existed in Flatland too, even though I, blind and senseless wretch, had no ability to see or touch it. So I am sure that there is a Fourth Dimension, which my Lord sees with the inner eye of thought.
Me: It must exist because of everything my Lord has taught me. Or has he forgotten what he himself taught his servant?
Me: In One Dimension, doesn’t a moving Point create a Line with Two terminal points?
Me: In Two Dimensions, doesn’t a moving Line create a Square with Four terminal points?
Me: And here in Three Dimensions, didn’t a moving Square create – in front of my own eye – a Cube, (such a blessed being) with Eight terminal points?
Me: And in Four Dimensions, doesn’t it follow that a Cube moving would create an even more divine shape with Sixteen terminal points? It will be a tragedy for Analogy and the Progress of Truth if it is not so!
Me: Look at the unquestionable pattern of the series: 2, 4, 8, 16 – Isn’t this a clear Geometrical Progression? Isn’t this – if I can quote my Lord’s own words – “strictly according to Analogy”?
Me: Again, didn’t you teach me yourself, my Lord, that in a Line there are Two outer Points, and in a Square there are Four outer Lines, and in a Cube there are Six outer Squares? The pattern is here again! 2, 4, 6, isn’t this an Arithmetical Progression?
Me: Doesn’t logic say that the more divine offspring of the Cube in the Land of Four Dimensions will have Eight outer Cubes, and isn’t this, as you have taught me to believe, “strictly according to Analogy”?
Me: O, my Lord, my Lord, I do not know if what I say is true, but I trust to my faith that it might be, and I beg your Lordship to tell me if my logic is right or wrong. If I’m wrong, I will give up the idea of the Fourth Dimension forever, but if I’m right, my Lord must listen to reason.
Me: So I ask you: Is it or is it not true that before now, your countrymen have also witnessed the appearance of Beings from a higher reality than their own – entering closed rooms, just as you entered mine, without opening any doors or window, and seeming to vanish at will? I will bet everything on the answer to this question. Tell me I’m wrong, that it’s not true, and I will never speak of it again. But please, give me an answer!
The Sphere, after a pause: There have been reports of such things. But no one can agree on what the facts are, and even when we look at the facts, the witnesses explain them in different ways.
The Sphere: And no matter how many witnesses there have been, no one has ever suggested that these visitors might be from the Fourth Dimension, so please stop these foolish questions, and lets get back to business.
Me: I was so sure of it! I was sure I was right! But please just have a little patience and answer me just one more question, you who are the Best Teacher in the World! Those who have appeared from nowhere, and gone away again back to nowhere, didn’t their sections also seem to grow and shrink as they vanished into the more Spacious Space where I am asking you to take me?
The Sphere, moodily: They vanished for sure, if they ever existed at all. But most people say that these “visitors” were only created by the witnesses’ disturbed imagination.
Me: Do they say that? Oh, please don’t believe them. Or if it is true, then that means this other Space is really Thoughtland, and I beg you to take me there, to that blessed Region where I will see the insides of all Solid things.
Me: There, in front of my delighted eye, I will watch a Cube, in strict accordance with Analogy, move in some new direction I don’t have a name for, and he will create an even more perfect shape than himself – a form with sixteen terminal Extra-Solid Angles, and Eight Solid Cubes for his outside Perimeter!
Me: And why stop there? Should we stop in the doorway to the Fifth Dimension and refuse to enter? No! Let us resolve to keep going higher!
Me: Bowing to our quest for knowledge, the gates of the Sixth Dimension will fly open, and after that the Seventh, and then the Eighth—
How long I would have kept this up, I don’t know. The Sphere tried, in a thundering voice, to silence me many times, threatening me with harsh punishments if I didn’t stop. But nothing could dam the river of my joyous, endless planning.
Maybe he was right to punish me, but I was only reacting to the amazing truths that he himself had revealed to me.
But it didn’t take long for the end to come.
My words were cut short by a crash that was both inside and outside of me at the same time, and it sent me flying through Space so quickly I didn’t have time to say anything else.
Down, down, down! I was falling so quickly, and I knew that returning to Flatland was to be my punishment.
I got one last look, one I will never forget, of that colorless, flat world which was going to once again be my whole Universe, spread out in front of my eye.
Then everything was dark. Then there was an all-consuming roar of thunder, and when I came back to awareness, I was once again a common, pitifully crawling Square, in my Study at home, hearing the Peace-Cry of my approaching Wife.
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